A painter sets a ladder up to reach the bottom of a second-story window 16 feet above the ground. The base of the ladder is 12 feet from the house. While the painter mixes the paint a neighbor's dog bumps the ladder which moves the base 2 feet farther away from the house how far upside of the house does the ladder reach
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When a ladder is placed on the house window at a distance away from the window a right angled triangle is formed with the ladder being the hypotenuse, the base length of the ladder being the base of the triangle and the distance from the ground to the top of the ladder being the height.
From the dimensions given we can get the length of the ladder using Pythagoras theorem.
12² + 16² =400
Length of ladder =√400=20feet.
When the ladder moves by 2 feet, the length of the base and the height changes but the length of the ladder remains the same.
In this case we have the new base as 12 + 2=14feet and the hypotenuse as 20feet.
We need to find the height using Pythagoras theorem :
20² - 14² =204
New height =14.28feet.
The height upside the house = Original height - new height.
16 - 14.28 = 1.72feet.
From the dimensions given we can get the length of the ladder using Pythagoras theorem.
12² + 16² =400
Length of ladder =√400=20feet.
When the ladder moves by 2 feet, the length of the base and the height changes but the length of the ladder remains the same.
In this case we have the new base as 12 + 2=14feet and the hypotenuse as 20feet.
We need to find the height using Pythagoras theorem :
20² - 14² =204
New height =14.28feet.
The height upside the house = Original height - new height.
16 - 14.28 = 1.72feet.
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